3 ms·

I think I agree with the crux of what you have to say, but do you have an example of people having non-transitive preferences? I can't think of one off the top

I think I agree with the crux of what you have to say, but do you have an example of people having non-transitive preferences? I can't think of one off the top of my head, and the classical economic argument is that non-transitive preferences would create a 'happiness pump' where I get stuck in a loop trading one thing for another and feeling good about the trade every time.

jonathanstrange 8y ago
These are called Spectrum Cases in the metaethical literature and have been discussed by Larry Temkin, Stuart Rachels, and others. Here is an example: A_1: One year of intense pleasure. A_2: Two years of slighly less intense pleasure than A_1. A_3: Four years of slightly less intense pleasure than A_2. . . . A_n: 2048 years of very low pleasure (slightly less intense than A_{n-1}). In every pairwise comparison we judge that A_{i+1} is better than A_i. However, we also judge that for some A_j in the spectrum, A_1 is better than A_j. Repeated applications of transitivity would contradict this, hence "better than" cannot be transitive. Before you dwell on the example, note that the same construction can be made with well-being and it may be made as realistic as you desire. As the size of his book already hints, Temkin (2012) discusses a vast number of variants in many evaluative domains. Money pumps under certainty are one argument against this. The problem is to explain what's wrong with your judgements in Spectrum Cases then. There are many other replies. John Broome suggests that "better than" is simply transitive by virtue of its meaning, but that misses Temkin's point and he's perfectly aware of this reply. You can also get away with giving up completeness, but the solution is not very convincing. It boils down to claiming that two adjacent items are incomparable somewhere in the spectrum, which is extremely implausible. In my personal opinion the only viable solution is a lexicographic approach that takes into account that two or more dimensions at play. I'll spare you the details, though. On a side note, there is an older tradition of arguing against the transitivity of "better than" based on measurement errors or the indistinguishability of adjacent items. This started with Luce (1956). In these cases, only the transitivity of "equally good" fails but "strict better than" remains transitive, hence this can be modelled with semiorders or interval orders. The representation theorems for utility representations change, but this is well-explored and not a problem. Spectrum Cases are much worse, if you buy into them, because they show that "strict better than" is not transitive.
- soVeryTired 8y ago
  That's really interesting, thanks!

jonathanstrange 8y ago

These are called Spectrum Cases in the metaethical literature and have been discussed by Larry Temkin, Stuart Rachels, and others. Here is an example: A_1: One year of intense pleasure. A_2: Two years of slighly less intense pleasure than A_1. A_3: Four years of slightly less intense pleasure than A_2. . . . A_n: 2048 years of very low pleasure (slightly less intense than A_{n-1}). In every pairwise comparison we judge that A_{i+1} is better than A_i. However, we also judge that for some A_j in the spectrum, A_1 is better than A_j. Repeated applications of transitivity would contradict this, hence "better than" cannot be transitive. Before you dwell on the example, note that the same construction can be made with well-being and it may be made as realistic as you desire. As the size of his book already hints, Temkin (2012) discusses a vast number of variants in many evaluative domains. Money pumps under certainty are one argument against this. The problem is to explain what's wrong with your judgements in Spectrum Cases then. There are many other replies. John Broome suggests that "better than" is simply transitive by virtue of its meaning, but that misses Temkin's point and he's perfectly aware of this reply. You can also get away with giving up completeness, but the solution is not very convincing. It boils down to claiming that two adjacent items are incomparable somewhere in the spectrum, which is extremely implausible. In my personal opinion the only viable solution is a lexicographic approach that takes into account that two or more dimensions at play. I'll spare you the details, though. On a side note, there is an older tradition of arguing against the transitivity of "better than" based on measurement errors or the indistinguishability of adjacent items. This started with Luce (1956). In these cases, only the transitivity of "equally good" fails but "strict better than" remains transitive, hence this can be modelled with semiorders or interval orders. The representation theorems for utility representations change, but this is well-explored and not a problem. Spectrum Cases are much worse, if you buy into them, because they show that "strict better than" is not transitive.

soVeryTired 8y ago
That's really interesting, thanks!